mgcv (version 0.8-2)

s: Defining smooths in GAM formulae

Description

Function used in definition of smooth terms within gam model formulae. The function does not evaluate a (spline) smooth - it exists purely to help set up a model using spline based smooths.

Usage

s(..., k=-1,fx=FALSE,bs="tp",m=0,by=NA)

Arguments

...

a list of variables that are the covariates that this smooth is a function of.

k

the dimension of the basis used to represent the smooth term. The default depends on the number of variables that the smooth is a function of. k should not be less than the dimension of the null space of the penalty for the term (

fx

indicates whether the term is a fixed d.f. regression spline (TRUE) or a penalized regression spline (FALSE).

bs

this can be "cr" for a cubic regression spline or "tp" for a thin plate regression spline. Only thin plate regression splines can be used for multidimensional smooths, so this argument only has an effect for univariat

m

The order of the penalty for this t.p.r.s. term (e.g. 2 for normal cubic spline penalty with 2nd derivatives). O signals autoinitialization, which sets the order to the lowest value satisfying 2m>d+1, where d is the number of covariates: this

by

specifies a covariate by which the whole smooth term is to be multiplied. This is particularly useful for creating models in which a smooth interacts with a factor: in this case the by variable would usually be the dummy variable

Value

• A list with the following items:
• term
  An array of text strings giving the names of the covariates that the term is a function of.
• bs.dim
  The dimension of the basis used to represent the smooth.
• bs.type
  The type of basis. 0 is cubic regression spline. 1 is thin plate regression spline. 0 can only be used for 1-d smooths.
• fixed
  TRUE if the term is to be treated as a pure regression spline (with fixed degrees of freedom); FALSE if it is to be treated as a penalized regression spline
• dim
  The dimension of the smoother - i.e. the number of covariates that it is a function of.
• p.order
  The order of the t.p.r.s. penalty, or 0 for auto-selection of the penalty order.
• by
  is the name of any by variable as text ("NA" for none).
• full.call
  Text for pasting into a string to be converted to a gam formula, which has the values of function options given explicitly - this is useful for constructing a fully expanded gam formula which can be used without needing access to any variables that may have been used to define k, fx, bs or m in the original call. i.e. this is text which when parsed and evaluated generates a call to s() with all the options spelled out explicitly.

Details

The function does not evaluate the variable arguments. It will correctly interpret calls like s(x,14|f) (results in pure regression spline smooth of one variable with a 14 knot cubic regression spline basis), s(x,z,20) (a penalized regression spline of 2 covariates using a 20 dimensional t.p.r.s. basis), etc. but this feature is purely for back compatibility reasons, and may not be maintained indefinitely.

References

Wood (2003) Thin plate regression splines. JRSSB in press.

See Also

gam

Examples

# example utilising `by' variables
library(mgcv)
set.seed(0)
n<-200;sig2<-4
x1 <- runif(n, 0, 1);x2 <- runif(n, 0, 1);x3 <- runif(n, 0, 1)
fac<-c(rep(1,n/2),rep(2,n/2)) # create factor
fac.1<-rep(0,n)+(fac==1);fac.2<-1-fac.1 # and dummy variables
fac<-as.factor(fac)
f1 <-  exp(2 * x1) - 3.75887
f2 <-  0.2 * x1^11 * (10 * (1 - x1))^6 + 10 * (10 * x1)^3 * (1 - x1)^10 - 1.396
f<-f1*fac.1+f2*fac.2+x2
e <- rnorm(n, 0, sqrt(abs(sig2)))
y <- f + e
# NOTE: smooths will be centered, so need to include fac in model....
b<-gam(y~fac+s(x1,by=fac.1)+s(x1,by=fac.2)+x2) 
plot(b,pages=1)